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. 2023 Apr 18;14(16):3884–3890. doi: 10.1021/acs.jpclett.3c00500

Oxygen-Driven Enhancement of the Electron Correlation in Hexagonal Iron at Earth’s Inner Core Conditions

Bo Gyu Jang †,‡, Yu He †,§, Ji Hoon Shim ∥,⊥, Ho-kwang Mao †, Duck Young Kim †,¶,*
PMCID: PMC10150722  PMID: 37071052

Abstract

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Earth’s inner core (IC) consists of mainly iron with some light elements. Understanding its structure and related physical properties has been elusive as a result of its required extremely high pressure and temperature conditions. The phase of iron, elastic anisotropy, and density–velocity deficit at the IC have long been questions of great interest. Here, we find that the electron correlation effect is enhanced by oxygen and modifies several important features, including the stability of iron oxides. Oxygen atoms energetically stabilize hexagonal-structured iron at IC conditions and induce elastic anisotropy. Electrical resistivity is much enhanced in comparison to pure hexagonal close-packed (hcp) iron as a result of the enhanced electron correlation effect, supporting the conventional thermal convection model. Moreover, our calculated seismic velocity shows a quantitative match with geologically observed preliminary reference Earth model (PREM) data. We suggest that oxygen is the essential light element to understand and model Earth’s IC.

The structure and composition of Earth’s core have long been a question of great interest. Although iron is generally believed to be the primary component of the Earth’s core, even the phase of iron is still controversial. Hexagonal close-packed (hcp) Fe is traditionally considered as the stable phase under the inner core (IC) conditions.1 Elastic anisotropy of the IC is regarded to originate from a preferred orientation of hcp Fe with a non-ideal c/a ratio.2 However, it was later shown that the c/a ratio of hcp Fe becomes almost ideal at a high temperature, resulting in the vanishing of the anisotropy.3,4 An alternative scenario based on body-centered cubic (bcc) Fe was proposed,3,5,6 in which a diffusion mechanism at high temperatures can make bcc Fe stable and give the anisotropy.6

The phase of iron at IC conditions is fundamentally important to model Earth’s geodynamo mechanism, because the electrical properties of hcp and bcc Fe are known to be very different. The electron correlation effect of transition metals, especially iron, should be considered properly at high-temperature conditions7−10 because a previous theoretical study found that the electrical conductivity from the electron–electron (e–e) scattering reaches ∼35% of that from the electron–phonon (e–ph) scattering in the case of hcp Fe at Earth’s core conditions.8 The electron correlation effect of bcc Fe is much larger than that of hcp Fe, and bcc Fe shows non-Fermi liquid behavior (or fully incoherent behavior) at IC conditions.9 This implies that the e–e scattering part can be even more significant in the bcc Fe case, and therefore, the corresponding thermal conductivity should be affected by the structure of iron.

Density and velocity of the IC in the preliminary reference Earth model (PREM)11 are smaller than those of pure iron. It is generally accepted that light elements should be involved to explain the density and velocity deficit of the IC.12 Although several light elements, such as S, O, Si, C, and H, have been suggested,13−18 it is still a matter of debate as a result of the lack of direct evidence. Among those elements, oxygen, one of the most abundant elements in Earth’s interior, has recently attracted attention as a prime candidate. The discovery of an oxygen-rich iron compound, FeO2, under deep lower mantle conditions suggests that there could be more oxygen under deep Earth conditions than we traditionally believed.19−21 Furthermore, the FeO partitioning model implied the potential existence of stable oxygen-enriched layers below the core–mantle boundary.22−24 A very recent experimental study suggests the stability of the FexO (x ≥ 3) close-packed structure under Earth’s core conditions.25 These studies support that oxygen should be considered in Earth’s core model.

Although the effects of these light elements on velocity deficit and conductivity from e–ph scattering have been studied from both the experimental and theoretical sides, there has been no detailed investigation of the effect of light elements on the phase of iron and conductivity from e–e scattering at IC conditions. For the realistic understanding of the thermal convection of IC, however, the contribution of light elements should be considered properly. The electrical conductivity from e–e scattering (electron correlation effect) can be sensitively affected by not only the phase of iron but also the volatiles in the compounds. Considering that iron oxides are strongly correlated compared to pure iron, the inclusion of oxygen in the IC model can modify the previous theoretical estimations on the thermal conductivity.

Here, we investigate the role of oxygen on the structural and physical properties of Earth’s IC. We find that FexO (x > 3) can be stabilized under IC conditions using ab initio calculations. This series of new iron oxide has a universal hcp Fe structure motif with an intercalated oxygen atom, indicating that oxygen atoms can stabilize the hcp phase at IC conditions. Intercalated oxygen atoms can make covalent bonds with Fe atoms, and this interaction can explain the anisotropy of the hcp phase. The existence of oxygen also enhances the electron correlation effect compared to pure hcp Fe. As a result, the electrical resistivity from the e–e scattering part can be greatly enhanced, indicating that the thermal conductivity can be smaller than the previous estimation on pure iron. The density and velocity deficit of the PREM model is also well-described by the existence of oxygen in the hcp Fe motif.

We first performed the structure prediction simulation of the Fe–O system at 300 GPa using the ab initio random structure searching (AIRSS) method based on density functional theory (DFT) calculations. We found that FexO (x ≥ 3) is on the convex hull line, showing energetic stability at IC pressure, as shown in Figure 1a. From Fe3O to Fe9O, they share a common structural motif, where the oxygen atom is intercalated between Fe atoms with a hcp structure, as shown in Figure 1b, implying that X-ray diffraction (XRD) patterns of the FexO series can be equivalent to that of pure hcp Fe. FexO possesses P3̅m1 space group for x = 2n (n > 1) and P6̅m2 space group for x = 2n + 1 (n ≥ 1), respectively. For x = 4n + 1 (n ≥ 1), strictly speaking, it possesses Amm2 space group, which is equivalent to a unit cell doubling of the P6̅m2 structure with a tiny distortion. The energy difference between P6̅m2 and Amm2 structures is merely ∼5 meV/f.u. for x = 5, 7, and 9. It is worth noting that our predicted crystal structures of x = 2, 3, and 9 cases are in good agreement with previous theoretical studies.26,27 Although we predicted the crystal structure up to x = 9, the obtained convex hull implies the stability of hexagonal-structured FexO with even large x, and the structure is converged to hcp Fe with a larger x limit. The structural stability at a high temperature is also confirmed by ab initio molecular dynamics (AIMD) calculations. The calculated elastic constants satisfy the stability conditions (Table S1 of the Supporting Information).

Figure 1.

Figure 1

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(a) Convex hull plot for the Fe–O system with the horizontal decomposition line into O and Fe. To verify the electron correlation effect on the formation energy, DFT + DMFT calculations were also employed. (b) Universal hexagonal crystal structure of FexO (x ≥ 3). FexO can be understood as oxygen-intercalated hcp Fe. The small amount of oxygen can stabilize the hexagonal structure of Fe. For better visualization of the hcp motif, Fe–Fe bondings beyond the unit cell (black solid lines) are also depicted.

However, standard DFT often is not enough to describe the electron correlation effect of Fe 3d orbitals. While one might expect the negligible contribution of the correlation effect with pressure, recent studies found that its effect is critical to describe the physical properties of iron even at the IC conditions.7−10 For example, previous DFT calculations predicted the R3̅m structure as the ground state of FeO at 300 GPa,26,27 but an experimental study reported a NiAs-type B8 phase at a low temperature and a CsCl-type B2 phase above 3000 K,28 clearly yielding an inconsistency.

To verify the correlation effect of Fe 3d orbitals on the energetic stability, we performed total energy calculations and revised the convex hull using the dynamical mean field theory (DMFT) calculation combined with DFT (U = 5 and 10 eV, J = 0.943 eV, and T ∼ 7000 K). Although the proper U value can be varied depending upon the composition, it is meaningless to compare the total energy with different U values. Therefore, we fixed the U value for whole compounds to calculate the convex hull line. Instead, we considered two cases, U = 5 and 10 eV, which are a reasonable value for moderate correlated pure Fe and strongly correlated FeO, respectively8,10,29−31 (Supporting Information). Interestingly, DFT + DMFT calculations give an excellent match with experimental data on determining the FeO phase, exhibiting that the B2 phase becomes the most stable phase at 300 GPa (Figure S2 of the Supporting Information). These results indicate the importance of the electron correlation effect on the physical properties of iron oxides, including the formation energy.

We found that hcp Fe is still more energetically favorable than bcc Fe by ∼1 eV/f.u., which is consistent with DFT calculations, and the energy difference is unlikely to be overcome by the entropy term. Although it was claimed that bcc Fe can be stabilized over hcp Fe at a high temperature as a result of the entropy term (S),6 the anomalous behavior of the entropy term with system size in the MD simulation is controversial.32 Recent MD simulations do not exhibit entropy anomalies depending upon the system size, and hcp Fe is more stable at IC conditions.32,33 The estimated entropy difference between bcc and hcp Fe is ∼1 J mol–1 K–1 at 360 GPa and 7000 K,32 resulting in TS ∼ 0.0725 eV/atom, which is not sufficient to overcome the enthalpy difference (∼1 eV/atom). The hexagonal FexO series (3 < x < 9) is still on the convex hull line within DFT + DMFT calculations, indicating the stability of FexO under IC conditions. Thus, hexagonal-structured iron oxides are preferred in the presence of oxygen.

As a representative example of our predicted iron oxides, Figure 2a shows the crystal structure of Fe9O. The distance between Fe atoms is aligned along the c direction, and it is similar to that of hcp Fe (black arrows), except for Fe atoms adjacent to the oxygen atom. The distance between Fe atoms above and below the O atom (∼2.60 Å) is much shorter than the others, indicating the strong interaction between Fe and O atom. One can find that the O atom is properly screened by the nearest Fe atoms, and the Fe–Fe distance is fully recovered to ∼3.40 Å of pure hcp Fe.

Figure 2.

Figure 2

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(a) Crystal structure of Fe9O at 300 GPa. The bond length between Fe atoms above and below the oxygen atom (Fe1–Fe1; red arrow) is shorter than the bond length between the second nearest Fe atoms (e.g., Fe1–Fe3 or Fe3–Fe5; black arrows). (b) d electron occupancy of Fe obtained from the DFT + DMFT calculation. As a result of the charge transfer from Fe1 to the oxygen atom, d occupancy of the Fe1 atom is smaller than those of other Fe atoms. (c) PDOS of Fe9O. PDOSs of Fe2–Fe5 show a dip feature at EF like pure hcp Fe, while PDOS of Fe1 shows a larger DOS at EF. (d) COHP analysis between O and the Fe1 atom. (e) Relative lattice constant depending upon the oxygen content. The c axis becomes shorter as the oxygen content increases.

Figure 2b shows the d electron occupancy of Fe atoms as a function of the distance from the O atom obtained from DFT + DMFT calculations. The numbers on Fe atoms in Figure 2a are assigned in order of the distance from the O atom, which correspond to the y ticks in Figure 2b. The d occupancy of FexO remains smaller than that of hcp Fe, monotonically increases as x increases, and eventually converges to that of hcp Fe (the vertical dashed line). The occupancy of the Fe1 atom is smaller than that of others as a result of the charge transfer from the Fe1 atom to the O atom. From the second nearest Fe atom from the O atom (Fe2), the occupancy is almost recovered to pure hcp Fe.

The partial density of state (PDOS) of Fe9O also clearly shows the interaction between O atom and neighboring Fe atoms as shown in Figure 2c. PDOSs of Fe atoms in FexO remain to be similar, except for that of the Fe1 atom (red line). Spectral function obtained from the DFT + DMFT calculation also exhibits equivalent behavior (Figure S3 of the Supporting Information). From the Fe2 atom, PDOS is almost identical to DOS of hcp Fe, which is consistent with occupancy analysis. At the Fermi level (EF), the Fe1 atom has a larger density than other Fe atoms. As a result of the charge transfer, Fe1 bands are shifted upward, making flat bands near EF (Figures S3 and S4 of the Supporting Information). The peak at around −12 eV observed in PDOS of both O and the Fe1 atom indicates the strong hybridization between them. Figure 2d shows the crystal orbital Hamilton population (COHP) analysis between O and the Fe1 atom, which can give insight on bonding properties.34 The overall shape of COHP indicates covalent bonding between O and the Fe1 atom rather than just ionic bonding between them. A notable bonding state is also shown in COHP at −12 eV.

Figure 2e shows the relative lattice constant change with respect to the oxygen content. For the direct comparison, the c lattice constant of each FexO (x = 5–9) compound is renormalized by the number of atoms in the unit cell along the c direction. As a result of the interaction between Fe and O atoms, the c lattice constant is affected sensitively by the oxygen content. The c lattice constant decreases ∼5% at 10% oxygen content (x = 9 case). The a lattice constant is less sensitive to the oxygen content, and it increases as the oxygen content increases. Thus, the existence of O atoms in hcp Fe enhances an anisotropic structural distortion not only along the c direction but in the ab plane. The bonding between Fe and the O atom explains elastic anisotropy at the IC. Previous studies on pure hcp Fe show that the c/a ratio becomes ideal as the temperature increases;3,4 however, the anisotropy can be induced in the presence of oxygen. As a result of the strong interaction between Fe and O, the c/a ratio of the hcp Fe motif can be anisotropic even at a high temperature. Although FexO would exist as a polycrystal at IC conditions, it could induce elastic anisotropy with a globally preferred orientation. Therefore, the existence of oxygen is an important key to understanding elastic anisotropy at IC conditions.

Pure hcp Fe shows a dip feature in its spectral function at EF (Figures S3 and S4 of the Supporting Information). As a result of the charge transfer and interaction between Fe1 and O atoms in Fe9O, however, flat bands occur near EF. As pointed out in the previous studies, a van Hove singularity enhances the correlation strength of systems, including bcc Fe.7,9,35 Flat bands near EF are well-observed in FexO, especially for x > 7 (Figure S4 of the Supporting Information). In addition, Fe1–Fe1 3d orbital overlap is strongly reduced because of interstitial oxygen, making the system more incoherent. Hence, we can expect the enhanced electron correlation effect in FexO compared to pure hcp Fe.

The resistivity from electron–electron scattering, ρe–e, of hcp Fe and Fe9O is computed with DFT + DMFT (U = 5 and J = 0.943 eV), as shown in Figure 3a. To compare to the previously calculated result, we adopt the IC density for hcp Fe and keep the density ratio between hcp Fe and Fe9O obtained from the 0 K DFT calculation for Fe9O. The calculated ρe–e of hcp Fe agrees well with the previous theoretical studies10 (directional resistivities are presented in Figure S5 of the Supporting Information). ρe–e of Fe9O is calculated to be higher than that of hcp Fe, and it monotonically increases with the temperature, reaching almost double the value at around 5800 K than that of hcp Fe. The resistivity increasing rate of Fe9O shows a slowdown above ∼4600 K, and that of hcp Fe keeps increasing up to 7000 K. We analyzed the temperature dependence of the inverse quasiparticle lifetime Γ, as shown in Figure 3b. Γ/kT of Fe9O almost converged above ∼4600 K, at which the resistivity increasing rate starts to decrease, signaling a fully incoherent regime.9,35,37 For the hcp Fe case, however, the fully incoherent regime does not appear up to 7000 K. Large ρ (or Γ) and the reduced temperature scale of Fe9O indicate that the existence of oxygen enhances the electron correlation strength of the hcp Fe motif.

Figure 3.

Figure 3

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(a) Resistivity from the e–e scattering part (ρe–e) from DFT + DMFT calculations. Our calculated result of hcp Fe agrees well with the previous results.10 ρe–e of Fe9O is much higher than that of pure hcp Fe. (b) Inverse quasiparticle lifetime Γ of hcp Fe and Fe9O. Γ/kT of hcp Fe shows almost T linear behavior up to 7000 K, while that of Fe9O is almost saturated at ∼4600 K. (c) Total resistivity (ρe–e + ρe–ph) depending upon the oxygen content. ρe–ph is taken from the previous study.36 Although ρe–e and ρe–ph both increase as the oxygen content increases, ρe–e is more sensitively affected by the oxygen content.

The total resistivity as a function of the oxygen content is shown in Figure 3c. Blue diamonds indicate computed ρe–e using DFT + DMFT based on the structure obtained from the DFT calculation at 300 GPa. The resistivity from electron–phonon scattering, ρe–ph, is taken from a previous study and exhibited by red squares with a dashed line.36 One can notice that ρe–e and ρe–ph are both enhanced by oxygen, and the e–e part is more sensitively changed. Black circles with a dashed line show the sum of ρe–e and ρe–ph. The resistivity of Fe9O is ∼20% larger than that of hcp Fe. It leads to a ∼17% reduction of conductivity by the inverse proportional relation between resistivity and thermal conductivity (Wiedemann–Franz law, κ = LT/ρ, where κ is the thermal conductivity and L is the Lorenz number).

Previous theoretical estimation on the thermal conductivity of pure hcp Fe at Earth’s core conditions is κ = 150–200 W m–1 K–1,8,10,38 which is too large to explain the thermal convection in the geodynamo (our estimation with the standard Lorenz number L = 2.44 × 10–8 W Ω K–2 is ∼200 W m–1 K–1). Including the oxygen effect, it can be reduced to 125–160 W m–1 K–1, which is consistent with a thermally convection-driven dynamo.39 The estimated thermal conductivity of Fe9O with the standard Lorenz number is ∼160 W m–1 K–1, but the Lorenz number can be reduced in comparison to hcp Fe as a result of the strong correlation effect.10,38

Finally, we investigated the elastic properties of hcp Fe and Fe9O under inner core conditions. A standard DFT calculation was first adopted to verify the oxygen effect clearly. The calculated density and velocity of hcp Fe at 300 GPa agree with the previous theoretical results. For Fe9O, which has 3.09 wt % oxygen, the density decreases by ∼3.2%, while the compression velocity (VP) increases by ∼1.9% (Table S1 of the Supporting Information). The electron correlation effect on the elastic properties was also verified using the DFT + DMFT calculation. The bulk modulus of hcp Fe at 300 GPa decreases ∼3.4%, which results in a ∼1.8% reduction of seismic velocity with the assumption that the shear modulus is also reduced by the same amount. However, the thermal lattice vibration effect is dominant over the electronic correlation effect. A previous ab initio molecular dynamics (AIMD) showed that the compression velocity decreases ∼11.3% at 5500 K compared to the 0 K result (Table S1 of the Supporting Information).

The elastic constant of hcp Fe and Fe9O obtained using AIMD calculations is shown in Table S2 of the Supporting Information. Our calculated elastic constants of pure hcp Fe at 360 GPa and 6000 K agree well with previous theoretical results.40,41 The compression (VP) and shear (VS) velocities in hcp Fe and Fe9O are calculated with the elastic constants and compared to the PREM data, as shown in Figure 4. As is well-known, the density of pure hcp Fe is higher than that of the PREM data. Fe9O (3.09 wt % oxygen) gives a much better result for density, indicating the possible existence of oxygen in Earth’s inner core. At 360 GPa and 6000 K, the density of Fe9O decreases by ∼3.8%, while VP increases by ∼1.3% compared to that of hcp Fe, like the simple DFT results. VS in Fe9O is still higher than that of the PREM data, and it can be further reduced when considering the presence of highly diffusive interstitial impurities.42

Figure 4.

Figure 4

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Seismic velocity of hcp Fe and Fe9O. Diamond, square, and circle points indicate the seismic velocity of PREM, hcp Fe, and Fe9O, respectively. The density and velocity of pure hcp Fe at 360 GPa are too high compared to the PREM data. For the Fe9O case, the existence of oxygen suppresses the density and velocity, resulting in better agreement with PREM data.

Here, we identify stable iron oxide compounds, FexO, at IC conditions using the DFT + DMFT calculation based on the AIRSS strategy. This iron oxide series have a universal hcp Fe motif with intercalated oxygen atoms, indicating that the existence of oxygen enhances the stability of the hcp Fe motif over the bcc Fe motif. We find that the interaction between Fe and O atoms can generate a strong contraction along the c axis, inducing elastic anisotropy observed in the experiment. Besides, the electronic correlation effect is strongly enhanced in the presence of oxygen. The small amount of oxygen drastically increases the electrical resistivity compared to the pure iron cases. As a result, the reduced thermal conductivity is consistent with a thermally convection-driven dynamo scenario. Finally, the seismic velocity is also investigated, and it is verified that oxygen can be an ideal candidate to explain the density velocity deficit at IC conditions.

Computational Methods

We conducted structure predictions for various compositions with two end member O and Fe atoms at the inner core pressure (300 GPa) using the AIRSS strategy43 combined with CASTEP software. As the exchange–correlation functional to DFT total energy calculations, we implemented Perdew–Burke–Ernzerhof (PBE),44 and a uniform k-mesh sampling of 0.04 Å–1 with a kinetic energy cutoff of 340 eV was used. The structures obtained from AIRSS were fully relaxed again with the VASP code,45 and the formation energies were cross-checked. PBE was also used for the exchange–correlation functional, and the plane-wave cut off was set to 500 eV. COHP analysis34 was performed on the basis of the VASP calculation.

DFT + embedded DMFT (eDMFT) code46 was employed to study the electron correlation effect of Fe 3d orbitals. DFT calculations were performed using the WIEN2k code, which uses the full-potential augmented plane wave method.47 PBE was used for the exchange–correlation functional. A total of 4000 k points were used to sample the first Brillouin zone of hcp Fe, and the same k-mesh density was used for other compounds. RKmax(Fe) was kept the same for all of the compounds for proper comparison of total energies to obtain formation energies. The real space projector is used to define the correlated subspace. All valence states within a large energy window (from −10 to 10 eV) with respect to the Fermi level were kept in the model and were allowed to hybridize with the correlated localized subset. U = 5 eV (and 10 eV) and J = 0.943 eV were used for Fe 3d orbitals. The density–density form (Ising type) of the Coulomb interaction was employed.

One of the ambiguous parts in the combination of the two methods (DFT + DMFT) is the double counting issue. One should subtract the part of correlations that is accounted for by both methods. The d occupancy of iron compounds under extreme conditions, such as the IC, is not definite, especially for the newly found compound, FexO. To avoid ambiguity, we used an exact double counting scheme,31 so that the overlap part can be determined precisely during the self-consistent cycle. The continuous time quantum Monte Carlo (CTQMC) method was used to solve the auxiliary quantum impurity problem.48 Up to 5 × 108 Monte Carlo steps were employed for each Monte Carlo run, and the total energy fluctuation as a result of Monte Carlo noise is smaller than 10 meV.

Ab initio molecular dynamics (AIMD) was adopted to calculate the elastic properties of Fe and Fe9O. A 4 × 4 × 2 supercell for Fe containing 64 atoms and a 4 × 4 × 1 supercell for Fe9O containing 160 atoms were used for AIMD simulations. The cutoff energy was set to 600 eV, and Brillouin zone sampling was performed at the Γ point. We determined the hydrostatic structures at different temperatures (4000–6000 K) and pressures (330 and 360 GPa) by conducting a grid of NVT ensemble simulations over volumes and temperatures. For each equilibrium structure of a different temperature, a 10 000 time step (10 ps) simulation was conducted to check for sure that the stress field is hydrostatic. The elastic constants of Fe alloys were calculated using the strain–stress method by distorting the equilibrium structures. Further details can be found in the Supporting Information.

Acknowledgments

The authors thank P. Zhang for fruitful advice on analytic continuation. This work is supported by the National Natural Science Foundation of China (Grants 11774015 and 41774101). Bo Gyu Jang was supported by a KIAS Individual Grant QP081301 at Korea Institute for Advanced Study (KIAS). Ji Hoon Shim acknowledges support by the Brain Pool program through the National Research Foundation of Korea funded by the Ministry of Science and Information and Communications Technology (ICT) under Grant NRF-2022H1D3A2A01096414. Ho-kwang Mao is supported by National Science Foundation (NSF) Grants EAR-1722515 and EAR-1447438. Duck Young Kim also acknowledges support from Shanghai Science and Technology Committee, China (No. 22JC1410300) and Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments, China (No. 22dz2260800).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.3c00500.

  • Calculation details, enthalpy difference between three FeO phase at 300 GPa, PDOS and imaginary self-energy for Fe9O and hcp Fe, k-resolved spectral function of FexO, directional resistivity of Fe9O and hcp Fe, and calculated elastic properties (PDF)

  • Transparent Peer Review report available (PDF)

The authors declare no competing financial interest.

Supplementary Material

jz3c00500_si_001.pdf (2.6MB, pdf)
jz3c00500_si_002.pdf (474.4KB, pdf)

References

  1. Tateno S.; Hirose K.; Ohishi Y.; Tatsumi Y. The Structure of Iron in Earth’s Inner Core. Science 2010, 330, 359–361. 10.1126/science.1194662. [DOI] [PubMed] [Google Scholar]
  2. Stixrude L.; Cohen R. E. High-pressure elasticity of iron and anisotropy of earth’s inner core. Science 1995, 267, 1972–1975. 10.1126/science.267.5206.1972. [DOI] [PubMed] [Google Scholar]
  3. Belonoshko A. B.; Ahuja R.; Johansson B. Stability of the body-centred-cubic phase of iron in the Earth’s inner core. Nature 2003, 424, 1032–1034. 10.1038/nature01954. [DOI] [PubMed] [Google Scholar]
  4. Gannarelli C. S.; Alfè D.; Gillan M. The axial ratio of hcp iron at the conditions of the Earth’s inner core. Phys. Earth Planet. Inter. 2005, 152, 67–77. 10.1016/j.pepi.2005.06.003. [DOI] [Google Scholar]
  5. Belonoshko A. B.; Skorodumova N. V.; Rosengren A.; Johansson B. Elastic Anisotropy of Earth’s Inner Core. Science 2008, 319, 797–800. 10.1126/science.1150302. [DOI] [PubMed] [Google Scholar]
  6. Belonoshko A. B.; Lukinov T.; Fu J.; Zhao J.; Davis S.; Simak S. I. Stabilization of body-centred cubic iron under inner-core conditions. Nat. Geosci. 2017, 10, 312–316. 10.1038/ngeo2892. [DOI] [Google Scholar]
  7. Hausoel A.; Karolak M.; Şaşıoǧlu E.; Lichtenstein A.; Held K.; Katanin A.; Toschi A.; Sangiovanni G. Local magnetic moments in iron and nickel at ambient and Earth’s core conditions. Nat. Commun. 2017, 8, 16062. 10.1038/ncomms16062. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Xu J.; Zhang P.; Haule K.; Minar J.; Wimmer S.; Ebert H.; Cohen R. E. Thermal Conductivity and Electrical Resistivity of Solid Iron at Earth’s Core Conditions from First Principles. Phys. Rev. Lett. 2018, 121, 96601. 10.1103/PhysRevLett.121.096601. [DOI] [PubMed] [Google Scholar]
  9. Pourovskii L. V.; Miyake T.; Simak S. I.; Ruban A. V.; Dubrovinsky L.; Abrikosov I. A. Electronic properties and magnetism of iron at the Earth’s inner core conditions. Phys. Rev. B 2013, 87, 115130. 10.1103/PhysRevB.87.115130. [DOI] [Google Scholar]
  10. Pourovskii L. V.; Mravlje J.; Georges A.; Simak S. I.; Abrikosov I. A. Electron-electron scattering and thermal conductivity of ϵ-iron at Earth’s core conditions. New J. Phys. 2017, 19, 073022. 10.1088/1367-2630/aa76c9. [DOI] [Google Scholar]
  11. Dziewonski A. M.; Anderson D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 1981, 25, 297–356. 10.1016/0031-9201(81)90046-7. [DOI] [Google Scholar]
  12. Poirier J.-P. Light elements in the Earth’s outer core: A critical review. Phys. Earth Planet. Inter. 1994, 85, 319–337. 10.1016/0031-9201(94)90120-1. [DOI] [Google Scholar]
  13. Tsuno K.; Frost D. J.; Rubie D. C. Simultaneous partitioning of silicon and oxygen into the Earth’s core during early Earth differentiation. Geophys. Res. Lett. 2013, 40, 66–71. 10.1029/2012GL054116. [DOI] [Google Scholar]
  14. Huang H.; Fei Y.; Cai L.; Jing F.; Hu X.; Xie H.; Zhang L.; Gong Z. Evidence for an oxygen-depleted liquid outer core of the Earth. Nature 2011, 479, 513–516. 10.1038/nature10621. [DOI] [PubMed] [Google Scholar]
  15. Mao Z.; Lin J. F.; Liu J.; Alatas A.; Gao L.; Zhao J.; Mao H. K. Sound velocities of Fe and Fe-Si alloy in the Earth’s core. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 10239–10244. 10.1073/pnas.1207086109. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Badro J.; Côté A. S.; Brodholt J. P. A seismologically consistent compositional model of Earth’s core. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 7542–7545. 10.1073/pnas.1316708111. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Sakamaki T.; Ohtani E.; Fukui H.; Kamada S.; Takahashi S.; Sakairi T.; Takahata A.; Sakai T.; Tsutsui S.; Ishikawa D.; Shiraishi R.; Seto Y.; Tsuchiya T.; Baron A. Q. R. Constraints on Earth’s inner core composition inferred from measurements of the sound velocity of hcp-iron in extreme conditions. Sci. Adv. 2016, 2, e1500802. 10.1126/sciadv.1500802. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Zhang Y.; Sekine T.; He H.; Yu Y.; Liu F.; Zhang M. Experimental constraints on light elements in the Earth’s outer core. Sci. Rep. 2016, 6, 22473. 10.1038/srep22473. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Hu Q.; Kim D. Y.; Yang W.; Yang L.; Meng Y.; Zhang L.; Mao H.-K. FeO2 and FeOOH under deep lower-mantle conditions and Earth’s oxygen-hydrogen cycles. Nature 2016, 534, 241–244. 10.1038/nature18018. [DOI] [PubMed] [Google Scholar]
  20. Liu J.; Hu Q.; Young Kim D.; Wu Z.; Wang W.; Xiao Y.; Chow P.; Meng Y.; Prakapenka V. B.; Mao H.-K.; Mao W. L. Hydrogen-bearing iron peroxide and the origin of ultralow-velocity zones. Nature 2017, 551, 494–497. 10.1038/nature24461. [DOI] [PubMed] [Google Scholar]
  21. Liu J.; Hu Q.; Bi W.; Yang L.; Xiao Y.; Chow P.; Meng Y.; Prakapenka V. B.; Mao H.-K.; Mao W. L. Altered chemistry of oxygen and iron under deep Earth conditions. Nat. Commun. 2019, 10, 153. 10.1038/s41467-018-08071-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Shahar A.; Schauble E. A.; Caracas R.; Gleason A. E.; Reagan M. M.; Xiao Y.; Shu J.; Mao W. Pressure-dependent isotopic composition of iron alloys. Science 2016, 352, 580–582. 10.1126/science.aad9945. [DOI] [PubMed] [Google Scholar]
  23. Pozzo M.; Davies C.; Gubbins D.; Alfè D. FeO Content of Earth’s Liquid Core. Phys. Rev. X 2019, 9, 041018. 10.1103/PhysRevX.9.041018. [DOI] [Google Scholar]
  24. Davies C. J.; Pozzo M.; Gubbins D.; Alfè D. Transfer of oxygen to Earth’s core from a long-lived magma ocean. Earth Planet. Sci. Lett. 2020, 538, 116208. 10.1016/j.epsl.2020.116208. [DOI] [Google Scholar]
  25. Liu J.; Sun Y.; Lv C.; Zhang F.; Fu S.; Prakapenka V. B.; Wang C.; Ho K.; Lin J.; Wentzcovitch R. M. Iron-rich Fe–O compounds at Earth’s core pressures. Innovation 2023, 4, 100354. 10.1016/j.xinn.2022.100354. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Huang S.; Wu X.; Qin S. Stability and anisotropy of (FexNi1–x)2O under high pressure and implications in Earth’s and super-Earths’ core. Sci. Rep. 2018, 8, 236. 10.1038/s41598-017-18678-z. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Weerasinghe G. L.; Pickard C. J.; Needs R. J. Computational searches for iron oxides at high pressures. J. Phys.: Condens. Matter 2015, 27, 455501. 10.1088/0953-8984/27/45/455501. [DOI] [PubMed] [Google Scholar]
  28. Ozawa H.; Takahashi F.; Hirose K.; Ohishi Y.; Hirao N. Phase transition of FeO and stratification in earth’s outer core. Science 2011, 334, 792–794. 10.1126/science.1208265. [DOI] [PubMed] [Google Scholar]
  29. Han Q.; Birol T.; Haule K. Phonon Softening due to Melting of the Ferromagnetic Order in Elemental Iron. Phys. Rev. Lett. 2018, 120, 187203. 10.1103/PhysRevLett.120.187203. [DOI] [PubMed] [Google Scholar]
  30. Ohta K.; Cohen R. E.; Hirose K.; Haule K.; Shimizu K.; Ohishi Y. Experimental and Theoretical Evidence for Pressure-Induced Metallization in FeO with Rocksalt-Type Structure. Phys. Rev. Lett. 2012, 108, 026403. 10.1103/PhysRevLett.108.026403. [DOI] [PubMed] [Google Scholar]
  31. Haule K. Exact Double Counting in Combining the Dynamical Mean Field Theory and the Density Functional Theory. Phys. Rev. Lett. 2015, 115, 196403. 10.1103/PhysRevLett.115.196403. [DOI] [PubMed] [Google Scholar]
  32. Schultz A. J.; Moustafa S. G.; Kofke D. A. No system-size anomalies in entropy of bcc iron at Earth’s inner-core conditions. Sci. Rep. 2018, 8, 7295. 10.1038/s41598-018-25419-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Godwal B.; González-Cataldo F.; Verma A.; Stixrude L.; Jeanloz R. Stability of iron crystal structures at 0.3–1.5 TPa. Earth Planet. Sci. Lett. 2015, 409, 299–306. 10.1016/j.epsl.2014.10.056. [DOI] [Google Scholar]
  34. Nelson R.; Ertural C.; George J.; Deringer V. L.; Hautier G.; Dronskowski R. LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory. J. Comput. Chem. 2020, 41, 1931–1940. 10.1002/jcc.26353. [DOI] [PubMed] [Google Scholar]
  35. Mravlje J.; Aichhorn M.; Miyake T.; Haule K.; Kotliar G.; Georges A. Coherence-Incoherence Crossover and the Mass-Renormalization Puzzles in Sr2RuO4. Phys. Rev. Lett. 2011, 106, 096401. 10.1103/PhysRevLett.106.096401. [DOI] [PubMed] [Google Scholar]
  36. De Koker N.; Steinle-Neumann G.; Vlček V. Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth’s core. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 4070–4073. 10.1073/pnas.1111841109. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Jang B. G.; Han G.; Park I.; Kim D.; Koh Y. Y.; Kim Y.; Kyung W.; Kim H.-D.; Cheng C.-M.; Tsuei K.-D.; Lee K. D.; Hur N.; Shim J. H.; Kim C.; Kotliar G. Direct observation of kink evolution due to Hund’s coupling on approach to metal-insulator transition in NiS2–xSex. Nat. Commun. 2021, 12, 1208. 10.1038/s41467-021-21460-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Pourovskii L. V.; Mravlje J.; Pozzo M.; Alfè D. Electronic correlations and transport in iron at Earth’s core conditions. Nat. Commun. 2020, 11, 4105. 10.1038/s41467-020-18003-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Driscoll P.; Bercovici D. On the thermal and magnetic histories of Earth and Venus: Influences of melting, radioactivity, and conductivity. Phys. Earth Planet. Inter. 2014, 236, 36–51. 10.1016/j.pepi.2014.08.004. [DOI] [Google Scholar]
  40. Martorell B.; Vocadlo L.; Brodholt J.; Wood I. G. Strong Premelting Effect in the Elastic Properties of hcp-Fe Under Inner-Core Conditions. Science 2013, 342, 466–468. 10.1126/science.1243651. [DOI] [PubMed] [Google Scholar]
  41. Li Y.; Vočadlo L.; Brodholt J. P. The elastic properties of hcp-Fe alloys under the conditions of the Earth’s inner core. Earth Planet. Sci. Lett. 2018, 493, 118–127. 10.1016/j.epsl.2018.04.013. [DOI] [Google Scholar]
  42. He Y.; Sun S.; Kim D. Y.; Jang B. G.; Li H.; Mao H.-k. Superionic iron alloys and their seismic velocities in Earth’s inner core. Nature 2022, 602, 258–262. 10.1038/s41586-021-04361-x. [DOI] [PubMed] [Google Scholar]
  43. Pickard C. J.; Needs R. J. High-Pressure Phases of Silane. Phys. Rev. Lett. 2006, 97, 045504. 10.1103/PhysRevLett.97.045504. [DOI] [PubMed] [Google Scholar]
  44. Perdew J. P.; Burke K.; Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. 10.1103/PhysRevLett.77.3865. [DOI] [PubMed] [Google Scholar]
  45. Kresse G.; Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186. 10.1103/PhysRevB.54.11169. [DOI] [PubMed] [Google Scholar]
  46. Haule K.; Yee C.-H.; Kim K. Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5. Phys. Rev. B 2010, 81, 195107. 10.1103/PhysRevB.81.195107. [DOI] [Google Scholar]
  47. Blaha P.; Schwarz K.; Tran F.; Laskowski R.; Madsen G. K. H.; Marks L. D. WIEN2k: An APW+lo program for calculating the properties of solids. J. Chem. Phys. 2020, 152, 074101. 10.1063/1.5143061. [DOI] [PubMed] [Google Scholar]
  48. Haule K. Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base. Phys. Rev. B 2007, 75, 155113. 10.1103/PhysRevB.75.155113. [DOI] [Google Scholar]

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